Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  long double n, sum = 0, count = 0, m, flag = 0, ans = 0, k;
  long double h, area, reqarea;
  cin >> n >> h;
  long double l = 0, r = 1.0, b, H;
  while (r - l > 0.00000001) {
    b = (l + r) / 2.0;
    if (h - b * b * h * n > 0.00000001)
      l = b + 0.00000001;
    else
      r = b - 0.00000001;
    count++;
  }
  H = b * h;
  long double a = b;
  cout << setprecision(15) << fixed << H << " ";
  for (int i = 0; i < n - 2; i++) {
    long double l = a, r = 1.0, b;
    while (r - l > 0.00000001) {
      b = (l + r) / 2.0;
      if (h - ((a + b) * (b * h - H) * n) > 0.00000001)
        l = b + 0.00000001;
      else
        r = b - 0.00000001;
    }
    H = b * h;
    a = b;
    cout << setprecision(15) << fixed << H << " ";
  }
  return 0;
}